If a function has a vertical asymptote at x = 3, what does the graph do as x approaches 3?

• A. It approaches a finite y-value
• B. It grows without bound as x approaches 3
• C. It becomes defined at x = 3
• D. The graph crosses the line x = 3

Answer: (B)

A vertical asymptote at x = 3 means the function is not defined at x = 3, and as x gets arbitrarily close to 3, the y-values grow without bound in magnitude. In other words, the graph shoots off toward infinity (positive or negative) near x = 3. This unbounded behavior is the hallmark of a vertical asymptote, so the description that fits is that the graph grows without bound as x approaches 3. The graph cannot be finite at x = 3, and it cannot cross the line x = 3 since that would require a point with x = 3 on the graph.